非扭转系统中偶数双生岛诱导的混沌传输的无剪切有效屏障
Shearless effective barriers to chaotic transport induced by even twin islands in nontwist systems
AI总结：
研究非扭转系统中偶数双生岛在无剪切环面破裂后形成的新型有效屏障，揭示了其依赖周期奇偶性的流形结构对混沌传输的抑制机制。
摘要：
几十年来，人们已知具有无剪切不变环面的系统（即非扭转 Hamilton 系统）具有阻碍混沌传输的屏障。这些屏障在扰动下不易破裂，因此它们存在的区域是寻找传输屏障的天然场所。我们描述了一种在无剪切环面破裂后依然存留的新型有效屏障。由于现象具有普适性，为方便起见，我们研究了 Standard Nontwist Map (SNM)，这是一种在相空间局部违反扭转条件的保面积映射。当存在偶周期双生岛时，非扭转系统中会出现这种新型屏障，这在 SNM 的广泛参数值范围内都会发生。在由规则和不规则轨道组成的相空间中，混沌轨迹的运动受到无剪切曲线（全屏障）以及由双曲点的稳定和不稳定流形形成的部分屏障网络的阻碍。作为退化系统，SNM 具有双生岛，因此也具有双生双曲点。我们证明，由流形形成的结构本质上取决于双生岛的周期奇偶性。在这种偶数情形下，由于不同双曲点的流形在偶极子结构顶部形成复杂链，且混沌轨迹通过该链的传输成为罕见事件，因此出现了名为 torus free barrier 的新结构。该结构影响传输的出现、混沌轨迹的逃逸盆地、传输机制和混沌鞍。奇周期轨道的情形则不同：我们发现在此情形下，最后一条不变曲线破裂后立即出现传输，这导致高传输场景，具有复杂的逃逸盆地边界和点分布不均匀的混沌鞍。
英文摘要：
For several decades now it has been known that systems with shearless invariant tori, nontwist Hamiltonian systems, possess barriers to chaotic transport. These barriers are resilient to breakage under perturbation and therefore regions where they occur are natural places to look for barriers to transport. We describe a novel kind of effective barrier that persists after the shearless torus is broken. Because phenomena are generic, for convenience we study the Standard Nontwist Map (SNM), an area-preserving map that violates the twist condition locally in the phase space. The novel barrier occurs in nontwist systems when twin even period islands are present, which happens for a broad range of parameter values in the SNM. With a phase space composed of regular and irregular orbits, the movement of chaotic trajectories is hampered by the existence of both shearless curves, total barriers, and a network of partial barriers formed by the stable and unstable manifolds of the hyperbolic points. Being a degenerate system, the SNM has twin islands and, consequently, twin hyperbolic points. We show that the structures formed by the manifolds intrinsically depend on period parity of the twin islands. For this even scenario the novel structure, named a torus free barrier, occurs because the manifolds of different hyperbolic points form an intricate chain atop a dipole configuration and the transport of chaotic trajectories through the chain becomes a rare event. This structure impacts the emergence of transport, the escape basin for chaotic trajectories, the transport mechanism and the chaotic saddle. The case of odd periodic orbits is different: we find for this case the emergence of transport immediately after the breakup of the last invariant curve, and this leads to a scenario of higher transport, with intricate escape basin boundary and a chaotic saddle with non-uniformly distributed points.
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